This Seiberg–Witten map approach to noncommutative gauge
theories is called universal enveloping algebra valued approach [1]}. It has been used to propose
noncommutative standard and grand unified particle physics
models [2]}, [3]} having the same degrees of freedom as in the commutative models. Renormalizability and scattering amplitudes using the Seiberg–Witten map have been studied e.g. in
[4]}, [5]}, [6]}, [7]}, either considering
a power series expansion in \(\theta \) 
or a \(\theta \) -exact approach (i.e. to all arders in \(\theta \) )
[5]}, [9]}, where the power series is instead in the gauge
coupling constant.
For recent literature on scattering amplitudes of noncommutative
particle models using the
Seiberg–Witten map see [10]} and references therein.
